Dana and Peter collect marbles and pencils. Peter has 48 less marbles than pencils. Peter has 2 times the number of marbles Dana has, and Dana has 25% more pencils than Peter. After Dana gives Peter all of her marbles and Peter gives Dana 75% of his pencils, Peter has 33 more marbles than pencils. Find the number of pencils Dana has at first.

Dana		Peter
Pencils	Marbles	Pencils	Marbles
2.5 u + 60	1 u	2 u + 48	2 u
+ 1.5 u + 36	- 1 u	- 1.5 u - 36	+ 1 u
4 u + 96	0	0.5 u + 12	3 u

100%+ 25% = 125% 

125% x 2 u
= ¹²⁵₁₀₀ x 2 u
= 2.5 u

125% x 48
= ¹²⁵₁₀₀ x 48
= 60 

75% x 2 u
= ⁷⁵₁₀₀ x 2 u
= 1.5 u  

75% x 48 
= ⁷⁵₁₀₀ x 48
= 36 

If another 33 pencils are given to Peter, he will have equal number of pencils and marbles in the end.
3 u = 0.5 u + 12 + 33
3 u - 0.5 u = 45
2.5 u = 45

1 u = 45 ÷ 2.5 = 18

Number of pencils that Dana has at first
= 2.5 u + 60
= 2.5 x 18 + 60
= 45 + 60
= 105
 
Answer(s): 105